Here’s the dilemma for the Republican Party: Tens of millions of its voters support a candidate, Donald J. Trump, who rejects the organization’s values, reviles its policies and wants to kick its leaders out of power.

How does a once-proud party begin to recover from that?

In the latest episode of The Run-Up, we look at how — and even whether — the GOP can remake itself after enduring 16 months with Mr. Trump as its nominee.

I speak with two Times reporters who know the party, its presidential candidates and voters better than anyone: Maggie Haberman and Nick Confessore.

The reckoning now underway, Ms. Haberman said, was a long time coming. “This isn’t a development that just happened with Trump,” she said. “Trump tapped into something.”

In the future, Mr. Confessore said, the party will have to decide who it really represents. “You can’t be both a party of center-right conservatism in a multicultural country in the future and be the party of toxic white resentment against declining power,” he said. “You can’t be both of those things. So either a leader emerges who can appeal to the better angels of people who feel resentful and left out and bring them along, or you have a third party, or a new party.”

The episode starts by exploring the state of the Republican establishment. And we end by examining the rebels trying to tear it down.

For that, I spoke with Ashley Parker, a reporter who travels with Mr. Trump and talks to his supporters every day.

She shared with me a tape from a conversation that she had with Paul Swick, whom she quoted in a recent story about the violence that could erupt if Hillary Clinton were to win on Election Day.

PARKER: If she does win, and you believe as Mr. Trump believes that it is a rigged election or it may have been stolen, what if anything do you do?

SWICK: I have no clue. I’m scared to answer that question because I know there’s a lot of people that are ready to raise up arms if that happens. And as much as that sounds like a good thing, it’s not. So it’s a scary situation.

PARKER: So you would not be among the people who would raise up arms?

SWICK: Oh no, I’m well armed. I would be one of those people. But it’s not something I pray for or hope for. It’s something I’m willing to do, but as a last resort.

How do I listen? Two ways

From a desktop or laptop, you can listen by pressing play on the button above.

Or if you’re on a mobile device, the instructions below will help you find and subscribe to the series.

On your iPhone or iPad:

1. Open your podcast app. It’s a pre-loaded app called “Podcasts” with a purple icon. (This link may help.)

2. Search for the series. Tap on the “search” magnifying glass icon at the bottom of the screen, type in “The Run-Up” and select it from the list of results.

3. Subscribe. Once on the series page, tap on the “subscribe” button to have new episodes sent to your phone free. You may want to adjust your notifications to be alerted when a new episode arrives.

4. Or just sample. If you would rather listen to an episode or two before deciding to subscribe, tap on the episode title from the list on the series page. If you have an internet connection, you’ll be able to stream the episode.

On your Android phone or tablet:

1. Open your podcast app. It’s a pre-loaded app called “Play Music” with an orange-and-yellow icon. (This link may help.)

2. Search for the series. Click on the magnifying glass icon at the top of the screen, search for the name of the series and select it from the list of results. You may have to scroll down to find the “Podcasts” search results.

3. Subscribe. Once on the series page, click on the word “subscribe” to have new episodes sent to your phone free.

4. Or just sample. If you would rather listen to an episode or two before deciding to subscribe, click on the episode title from the list on the series page. If you have an internet connection, you’ll be able to stream the episode.